function diff = J_n_p( m, param)
    % calculates J\prime(m) in natural wastage region
    diff = (1-param.omega_1)./rho_fun( 1, 'N', param) ...
            + param.J_1*m.^(param.gamma_N_1).*param.gamma_N_1./m ...
            + param.J_2*m.^(param.gamma_N_2).*param.gamma_N_2./m;

end